Precise Rates in the Generalized Law of the Iterated Logarithm in ${\mathbb{R}}^m$
Received:February 06, 2017  Revised:August 04, 2017
Key Word: precise rates   law of iterated logarithm   complete convergence   i.i.d. random vectors  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.61662037) and the Scientific Program of Department of Education of Jiangxi Province (Grant Nos.GJJ150894; GJJ150905).
Author NameAffiliation
Mingzhou XU School of Information and Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China 
Yunzheng DING School of Information and Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China 
Yongzheng ZHOU School of Information and Engineering, Jingdezhen Ceramic University, Jiangxi 333403, P. R. China 
Hits: 2844
Download times: 1951
Abstract:
      Let \{$X$, $X_n$, $n\ge 1$\} be a sequence of i.i.d. random vectors with ${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$ and ${\rm Cov}(X,X)=\sigma^2I_m$, and set $S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. For every $d>0$ and $a_n=o((\log\log n)^{-d})$, the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of ${\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$.
Citation:
DOI:10.3770/j.issn:2095-2651.2018.01.010
View Full Text  View/Add Comment  Download reader